Weak perturbations of the p-Laplacian

Abstract

We consider the p-Laplacian in R^d perturbed by a weakly coupled potential. We calculate the asymptotic expansions of the lowest eigenvalue of such an operator in the weak coupling limit separately for p>d and p=d and discuss the connection with Sobolev interpolation inequalities.

20 pages

References in corpus (2)

• Weakly coupled bound states of Pauli operators
• The weakly coupled fractional one-dimensional Schrödinger operator with index $1<\alpha \le 2$

Cited by in corpus (1)

• On the $p$-Laplacian with Robin boundary conditions and boundary trace theorems